A MILLION MPH

in antiquity it was a commonly held belief that the earth was stationary after all if we were moving surely we would feel it today our modern understanding of the cosmos dictates that we're not just moving we're accelerating and hurtling through space at nearly a million miles per hour so please join me professor kipping as we explore our motion through space and why ultimately the question itself is far subtler than one might first imagine [Music] how fast are you moving it's a question so simple in form yet one so nuanced and subtle to directly answer because what do we really mean by that question are we talking about speed or are we talking about velocity or perhaps even acceleration and relative to what are we defining this motion for millennia we thought the earth was at rest because after all we didn't feel ourselves moving so of course this made sense to ancient thinkers ride on a horse float down the river or even skateboard round new york city and you can feel yourself moving you can feel the wind in your hair the bumps and the road and the pull as you turn from side to side but lying in bed each night we don't feel ourselves moving it was the study of the stars and the planets that revealed the fallacy of this geocentric view that it is not the entire cosmos that moves in some elaborate dance to accommodate us as special privileged observers in the universe but rather it was us that was moving all along we are the ones in motion beautifully shown here through a time lapse of the sky where the rotation of the earth giving us our days and nights is clearly seen but rotation is just one way in which we are moving there's many other ways in which we can define our cosmic motion so what kind of speeds are we talking about here well first off let's talk about rotation the 24 hour spin of our planet now here when we're talking about speed we really mean our motion relative to the center of the planet the very core of the earth to make things simple let's imagine that we live along the equator of the earth represented by this piece of twine here and further i'm going to imagine that we live in the city of kampala located here in uganda now let's set the earth in motion now to calculate the speed on the equator we just need to remember the defining formula that it equals the distance covered divided by the time taken and so here the distance covered is going to be the circumference around the earth marked by that piece of string and in fact the center of that piece of string goes through the center of the earth and so that means that this circle is technically a great circle so if we take this piece of string off the earth and measure its length we will get a distance of 24 900 miles and kampala travels that distance once every day or once every 24 hours so that means that the speed 24 900 divided by 24 equals over 1 000 miles per hour now i say miles per hour but actually physicists usually prefer to use meters per second but for the sake of this video we will stick to more intuitive units like miles per hour now the plot thickens because your speed is actually going to be slower if you live away from the equator so let's imagine that we live over here in anchorage alaska at 60 degrees north latitude now the circle that you trace out is much smaller and it doesn't pass through the center of the earth this is a small circle not a great one comparing to the equator the circumference of this circle is cosine 60 degrees times smaller or 50 percent one-half as big since the time it takes anchorage to complete one full rotation of the earth is the same as that as kampala or indeed anywhere else on the earth it's 24 hours then that means that the distance has halved but the time is the same and so therefore the speed is halved and if we live even further away from the equator and one of the poles then actually you would just be spinning in place your speed at least relative to the center of the earth would be zero so it makes perfect sense why you don't feel this rotational motion if your name is santa claus but for everybody else surely we should be feeling this spinning motion at speeds of a thousand miles per hour you often hear it erroneously said even on many science channels here on youtube that the reason why we don't feel this speed is because it isn't changing but on the equator you're going about a thousand miles an hour in a circle every day you don't feel it for the same reason you aren't stuck in your seat while a plane is flying speed is relative you only feel it when it changes but clearly this is wrong because if you sit on a merry-go-round and it spins round at a constant speed you will absolutely feel that motion in fact to such a degree that you can make yourself nauseous and throw up when you get off the merry-go-round in fact go in a faster centrifuge and a constant spin rate a constant speed can cause you to black out whether you're on a merry-go-round or the earth your speed is constant but critically the direction of motion is constantly changing and that means that your velocity is changing and speed and velocity are subtly different because the latter cares about direction but the former does not so to come back to our original point if the velocity isn't changing like sitting on an airplane cruising through the air then indeed you can't feel the motion but if the velocity is changing even though the speed is constant then you have an acceleration and accelerations we do feel every time you drive your car and turn a corner at constant speed your velocity is changing and thus you feel the motion likewise throwing your foot on the brakes causes a sharp acceleration in the opposite direction to your velocity which you can also feel isaac newton taught us that force equals mass times acceleration so any acceleration manifests as a force that we perceive on our bodies so why don't we feel this acceleration here on the earth well in a way we actually do when you bank a corner in your car if i turn to the right i'll feel a force pulling me to the left so imagine again you lived in kampala and i'm now looking at the earth from above this same force known as the centrifugal force should be pushing you outward from your direction of motion and that means that you are actually feeling a force that's trying to lift you up into space which begs the question why aren't our kampalan residence just sort of floating off into space well remember our physics 101 that when we are calculating the motion of an object we have to consider all of the forces acting on that body and critically there is another very important force acting out a compelling resonance and that is gravity at the equator the force of gravity acts in precisely the opposite direction to the centrifugal force the acceleration caused by gravity is famously about 10 meters per second per second simply known as one g and here the centrifugal acceleration is about .03 meters per second per second or three thousandths of a g so despite the fact that your speed is over a thousand miles per hour your velocity is changing at such a minuscule rate that the imposed g-force is a tiny fraction of that of gravity yet more the fact that this force is a constant and acts in the opposite direction to that of gravity makes it imperceptible the only real effect of this is that the earth's rotation actually causes you to weigh slightly less than you otherwise would in fact the compalon residence would weigh about 10 ounces more of the earth stop spinning and for those away from the equator the centrifugal force is accordingly diminished indeed the fact that there is less force acting on the equator than the poles causes the earth to take on a slightly non-spheroidal shape bulging out at the sides like a planet in need of a diet the earth modifies her shape naturally finding an equilibrium point where the net downward force is approximately the same everywhere this balance between the centrifugal and the gravitational force raises an interesting question could we imagine a planet that is spinning much faster than the earth so much so that the centrifugal force is equal and opposite to that of gravity if this were true surface rocks would just float up into the air behaving as if they're in a zero g environment now of course this would require a much shorter day a special rotation rate known as breakup speed for the earth that would correspond to a day of 1.4 hours dramatically faster than our current rotation speed on such a planet you could trivially push off the equatorial surface and just float off into deep space rocket launches would be far easier and surface rocks would similarly float along with you now the book of the earth would stay down just due to the resistive internal strength of the rocks themselves but if we made the earth spin much faster than 1.4 hours then even eventually these would break apart and fly off into space the breakup speed is a simple formula that just balances gravity with the centrifugal force and thus we can calculate it for any planet or asteroid that we wish remarkably if we look at asteroids in the solar system we see that there's a clear deficit of asteroids rotating faster than their calculated breakup speeds and of course this makes sense if they are just powers of rubble loosely held together however there are some asteroids spinning faster than this breakup speed and that tells us that they must be solid bodies of rock and metal potentially interesting space mining targets for the future all together then the fact that we don't feel this rotational speed on the earth is not because our speed is constant nor because there are no forces acting on us no in fact there are forces acting on us it's just that those forces aren't miniscule in comparison to gravity and look if that wasn't true then you would be floating off into space a thousand miles per hour sounds impressive but it's actually just one way in which we are moving through space so let's consider the others it's usually at this point that videos like this will start to talk about the earth's motion around the sun but if we skip ahead to that we actually forget about a more nuanced effect we often say that the moon orbits the earth but from the moon's perspective it is the earth that orbits the moon and from the sun's perspective both of them are wrong they're orbiting each other dancing around a common center of mass located between us following the law of pivots this balancing point lies about 900 miles away from the earth's center which is actually still inside the earth that's because the earth is of course much heavier than the moon by a factor of 81. nevertheless the earth is truly in orbit of this point and so we can trace out this circle of circumference 2 pi multiplied by 2 900 miles once every 27 days that's the orbital period of the earth moon pair this wobbling causes us to move at a modest speed of about 28 miles per hour roughly the speed limit in most of new york city whereas the earth's rotation causes an acceleration of 3 millig this wobbling motion causes a much smaller acceleration just 3 micro g which is so small we can't even detect it so again it should be of no surprise that we do not feel this force the fact that the earth wobbles around this common center of mass is actually one of the tricks that we developed and use here in the cool world's lab to look for moons outside of the solar system because if an exoplanet has a large moon then it too will undergo this slight wobbling motion and we can detect that in its orbital path and so you can probably understand why to me overlooking this effect was never going to happen on this channel it's one of the most powerful techniques we have to search for alien moons so how does our rotational speed of a thousand miles per hour and uh lunar wobble speed of 30 miles per hour compared to our orbital speed around the sun well to calculate that we can just do what we did before we just got a handy piece of string here although now a very very very long piece of string and we trace it around the earth's orbit around the sun and divide it by the time it takes for us to complete that journey dividing this distance by one year the orbital speed of the earth comes out at 66 628 miles per hour however once again the acceleration is pitiful just 600 micro g now these high speed numbers that i'm throwing around here they're not just here to impress you to startle you they're actually useful to us when we conduct space flight when we plan a rocket launch you can time the launch such that the rocket speed gets an extra 1000 miles per hour just from the earth's rotation naively this would mean launching in the dead of night when the rotational velocity lines up with the orbital velocity in practice though launches need to be earlier than this to have time to get out of the atmosphere and then accelerate out of the earth's gravitational field the earth's speed is also useful to us when we perform gravity assists also known as the slingshot maneuver when one approaches a moving gravitational body such as the earth you can kind of imagine bouncing off the gravitational field like a ball bouncing off a moving wall it increases your speed nasa's juno spacecraft actually did this back in 2013 returning back to the earth for a close flyby where it increased its speed by 16 330 miles per hour which equals a respectable 25 percent of the earth's orbital speed the theoretical maximum speed boost you can get from these gravity assists equals precisely twice the orbital speed of the planet you're conducting the maneuver around but if you did that you would actually end up with so much speed that you would leave the solar system altogether you would exceed the escape velocity and so now you can't come back around and get a second or a third speed boost and this really explains why going into interstellar space isn't that difficult but doing so at speeds much higher than that of the orbital speeds of the solar system planets is very very challenging in our quest to understand our speed let's now leave the solar system all together the sun itself moves through space being pooled by the various nearby stars in any discussion of motion we have to have a point of comparison and in the local solar neighborhood which is about 100 parsecs or some 300 light years across that point of reference is defined as the local standard of rest or lsr in this frame of reference the sun has a fairly typical speed compared to that of its neighbors some 15 kilometers per second or 30 000 miles per hour so we have the sun moving relative to the lsr at some 30 000 miles per hour and on top of that we have the earth which moves around the sun at an additional 67 000 miles per hour but it turns out we can't just add these two numbers together because the trajectories don't quite align there's about a 60 degree angle between the two yet more our velocity around the sun is clearly going to be different depending on what day of the year it is but putting this together the planets seem to trace out a kind of helical pattern on their voyage through the galaxy this is sometimes exaggerated in popular depictions often appearing as though the planets lag behind the sun whereas in reality the planets often lead due to the inclined angle of the solar system's trajectory but the helical trace is broadly true and one can't help but be reminded of the shape of dna in fact if we had two planets sharing the same orbit at opposite phases which isn't particularly stable it would in fact trace out the double helix shape through the stars who knows perhaps there is a cosmic art piece flying through the stars depicting such a system the sun's motion through the lsr is complicated because it is feeling the gravitational pull of many different stars which are themselves in motion one approximate model which i'll link to down below estimates that the sun's motion can be modeled as a kind of epicyclic path through the lsr as shown here the sun bounces up and down the galactic midplane by about 100 parsecs every 80 million years or so as well as following an elliptical path within the plane around the local region of stars and of course this entire lsr is itself in motion orbiting the center of the galaxy on approximately circular path with an orbital speed of some 250 kilometers per second or that's about 560 000 miles per hour now that sounds like a frighteningly impressive number but it's actually less than 0.1 percent the speed of light and thus we don't have to worry about relativistic effects here at this speed it takes the sun between 225 and 250 million years to complete a full orbit around the galaxy what we might call a galactic year now since the sun is 4.6 billion years old that equates to about 20 galactic years old so i guess the sun is almost ready to legally buy its first beer it will probably live into its mid 40s on this scale at which point it will leave behind a white dwarf tombstone in fact at this speed the sun travels about a tenth of a light year every century which is comparable to human lifetimes and the sun has traversed a distance of nearly four million light years during its entire lifetime and so in a very real way the sun the planets and indeed the other stars around us are all intergalactic spaceships who have traversed the galaxy many times over and so perhaps for a very long-lived civilization they might not build spaceships after all why should they when they live on one the final frontier in our quest for speed is to leave the milky way altogether it's at this point that the definitions of speed get harder to define for example the nearest major galaxy andromeda is seemingly charging towards us at 110 kilometers per second or some 250 000 miles per hour in about 4.5 billion years a time when the sun will be turning into a red giant the two galaxies will merge forming a new milk dromeda super galaxy but from andromeda's perspective they are not moving it is us the milky way that is charging towards them at this same speed and there's no cosmic standard to judge who is right and who is wrong here it's all just a matter of perspective and this gets at the very heart of einstein's special theory of relativity which tells us that there's no such thing as absolute space or time it's just relative to something else einstein's theory starts with the postulate that the speed of light is the same in all inertial frames of reference and really more generally that the laws of physics are the same in all such frames so we can talk about the milky way's speed relative to any nearby galaxy but it's ultimately somewhat arbitrary because all definitions of speed are always relative to something else after all when you walk down the carriage of a 50 mile per hour train are you moving at 3 miles per hour or 53 miles per hour both are right it just depends what you're comparing to but one example might at first seem to defy this the cosmic microwave background or the cmb this is the radiation that was produced by the hot primordial soup of the early universe just 380 000 years after the big bang that time corresponds to the epic when the universe became transparent to light for the first time because before that it was largely ionized creating a kind of thick fog that prevented light from traversing space the cmb radiation is all around us we are bathed in its light it comes from every direction up down left right and that's because the universe itself is all around us these photons have traveled many billions of light years to finally reach us they are distant and ancient messengers from those earliest of times when the cmb photons were emitted the universe was about 3000 kelvin a temperature that was encoded within the photons themselves but because of the enormous expansion of the universe the wavelengths of these light waves have been stretched out so much so that the photons now appear much cooler about 2.7 kelvin what's striking though is that the temperature is not 2.7 kelvin in every direction there's a few milli kelvin difference with a clear pattern known as the cmb dipole we see that some of the cmb photons are more blue shifted than average and others are red-shifted and this pattern and elegant symmetry that we see in the cmb dipole is explained by a simple answer that we are moving with respect to the cmb rest frame at a speed of 370 kilometers per second or 830 000 miles per hour so nearly a million miles per hour indeed if we take the milky way galaxy as a whole it is moving relative to the cmb rest frame at 1.3 million miles per hour the cmb might at first then seem to offer a special frame of reference in essence it's the rest frame of the entire universe it's like we're in a bath of photons but that bath has a directional motion to it like a breeze blowing against our skin the cmb rest frame is a fascinating concept but truthfully it doesn't have too much physical significance and it doesn't obviate einstein's work because really einstein just said that the laws of physics are the same in all frames and that's still true ultimately defining a speed with respect to the c and b is no different to defining our speed respect to the center of the earth or the center of the sun or the center of the galaxy they are all just equally valid benchmarks against which one could define a speed and so our quest to measure our speed comes to the conclusion that in many ways the answer doesn't really matter in one frame we're moving in a million miles per hour but in the other we're not moving at all it's the relationship between things that matters their relative nature and influence upon one another astronomy teaches us that there is no center of the universe speeds are only relative there's no absolute space there's no absolute time the judge of the universe only cares about comparisons and so perhaps when we come to judge ourselves with this in mind we should try to find a worthy ideal against which to compare ourselves to to strive towards so until the next video stay thoughtful and stay curious thank you so much for watching everybody i just want to give a quick thank you to our latest coords donor that is alex davao thank you so much for your support alex if you too want to help us make these videos and the research in our team the cool world's lab then make sure you click the link up above see you around the galaxy you

Channel: Cool Worlds

Views: 450,155

Keywords: Million MPH, Million Miles per hour, how fast are you moving, how fats are you moving through space, how fast are we moving, how fast is earth, how fast is the sun, what speed is the earth, what speed are we, speed through the galaxy, speed through the universe, extreme speed universe, universe speed, galactic speed, speed through space, david kipping, cool worlds, astronomy, astrophysics

Id: 0HrF2OR0-Sc

Length: 25min 50sec (1550 seconds)

Published: Sat May 01 2021